Question: Multiply the following complex numbers: $({-1-3i}) \cdot ({-4+i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-3i}) \cdot ({-4+i}) = $ $ ({-1} \cdot {-4}) + ({-1} \cdot {1}i) + ({-3}i \cdot {-4}) + ({-3}i \cdot {1}i) $ Then simplify the terms: $ (4) + (-1i) + (12i) + (-3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-1 + 12)i - 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-1 + 12)i - (-3) $ The result is simplified: $ (4 + 3) + (11i) = 7+11i $